It has been known that air-fuel ratio of exhaust gas emitted from an internal combustion engine is detected by an exhaust gas sensor (for example, air-fuel ratio sensor), and a fuel injection quantity is feedback-controlled so that the detection value of the exhaust gas sensor agrees with a target air-fuel ratio. In a case of a multi-cylinder engine, it is likely that a variation in intake air quantity may occur between cylinders due to a difference in shape of each intake manifold and/or a variation in intake valve operation. In a case of multi point injection (MPI) system, it is likely that the fuel injection quantity in each cylinder may be different form each other due to an individual difference of a fuel injector provided to each cylinder. Such a difference in intake air quantity and/or fuel injection quantity between cylinders may increase a difference in air-fuel ratio in each cylinder and deteriorates an accuracy of air-fuel ratio control.
In order to solve the above problems, it is proposed that an air-fuel ratio of each cylinder is estimated based on a detection value of the exhaust gas sensor and the air-fuel ratio (fuel injection quantity) of each cylinder is corrected based on the estimated air-fuel ratio so that the variation in air-fuel ratio between cylinders becomes smaller. Japanese Patent No. 3683355 (U.S. Pat. No. 5,806,506) shows an air-fuel estimating system in which an observer which observes an internal condition of an engine is established based on a model representing a behavior of the exhaust gas. Based on detection value of an exhaust gas sensor (air-fuel ratio sensor) which is disposed at a confluent portion of the exhaust gas, the air-fuel ratio of each cylinder is estimated.
In such a system having an exhaust gas sensor disposed at a confluent portion of exhaust gas, due to a difference in flow direction of exhaust gas discharged from each cylinder, a difference in length of an exhaust manifold of each cylinder and an interval of combustion in each cylinder, an output characteristic of the exhaust gas may be varied with respect to each cylinder. That is, it is likely that a difference in detectability of the exhaust gas sensor may occur with respect to air-fuel ratio of each cylinder. The air-fuel ratio of each cylinder can not be estimated with high accuracy.